Flexible flat packages such as standard envelopes, padded envelopes, and bubble mailers are commonly used to ship inventory items. Typically, the inventory items are placed into the packages by hand and the packages are sealed by hand, which is a relatively time consuming and labor intensive process. However, automating this process presents several challenges. For example, the inventory items should be placed into the package in a proper orientation so as to not impede the edges of the package that are subsequently sealed. This is made more difficult by the fact that flexible flat packages tend to deform based on the size and shape of the inventory items as the inventory items are placed therein.